For Dhingra Classes, Nashik
Subject: Mathematics
Class: VIII
Maximum Marks: 80
Time Allowed: 3 Hours

🧭 General Instructions

• All questions are compulsory.

• Marks are indicated against each question.

• Answers should be written in a clear and stepwise manner.

• Use of calculator is not permitted.

📝 SECTION A: MCQ (20 × 1 = 20 Marks)

1. The value of (9⁴ ÷ 9²) × 9⁻¹ is:
(a) 9 (b) 9² (c) 9³ (d) 9⁰
Ans: (a) 9

2. The Babylonian number system was based on:
(a) Base 10 (b) Base 12 (c) Base 60 (d) Base 20
Ans: (c) Base 60

3. A quadrilateral with exactly one pair of parallel sides is called:
(a) Parallelogram (b) Trapezium (c) Rhombus (d) Rectangle
Ans: (b) Trapezium

4. The digital root of 856 is:
(a) 1 (b) 2 (c) 3 (d) 4
Ans: (a) 1

5. Using the distributive property, 38 × 101 equals:
(a) 3838 (b) 3800 (c) 3880 (d) 3830
Ans: (a) 3838

6. If 12 men can build a bridge in 10 days, how many men are needed to build it in 8 days?
(a) 14 (b) 15 (c) 16 (d) 18
Ans: (b) 15

7. In a right triangle, if the legs are 9 cm and 40 cm, the hypotenuse is:
(a) 41 cm (b) 42 cm (c) 43 cm (d) 44 cm
Ans: (a) 41 cm

8. The set {x : x is an even prime number} is:
(a) Empty set (b) Singleton set (c) Infinite set (d) Universal set
Ans: (b) Singleton set

9. If A = {1, 2, 3, 4} and B = {3, 4, 5, 6}, then A ∩ B is:
(a) {1, 2} (b) {3, 4} (c) {5, 6} (d) {1, 2, 3, 4, 5, 6}
Ans: (b) {3, 4}

10. The value of (5⁻¹ × 5³) ÷ 5² is:
(a) 1 (b) 5 (c) 25 (d) 125
Ans: (a) 1

11. The Chinese number system used which type of numerals?
(a) Rod numerals (b) Roman numerals (c) Arabic numerals (d) Mayan numerals
Ans: (a) Rod numerals

12. If each interior angle of a regular polygon is 135°, the number of sides is:
(a) 6 (b) 7 (c) 8 (d) 9
Ans: (c) 8

13. Which of the following is NOT a Baudhāyana triple?
(a) (5, 12, 13) (b) (8, 15, 17) (c) (7, 24, 25) (d) (6, 9, 12)
Ans: (d) (6, 9, 12)

14. If 15 oranges cost ₹90, then the cost of 25 oranges is:
(a) ₹120 (b) ₹150 (c) ₹180 (d) ₹200
Ans: (b) ₹150

15. The value of 2⁻⁵ × 2⁵ is:
(a) 0 (b) 1 (c) 2 (d) 32
Ans: (b) 1

16. In a kite, the diagonals:
(a) Are equal (b) Bisect each other (c) Are perpendicular (d) Are parallel
Ans: (c) Are perpendicular

17. The expansion of (a − 4)(a + 7) is:
(a) a² + 3a − 28 (b) a² − 3a − 28 (c) a² + 11a − 28 (d) a² + 3a + 28
Ans: (a) a² + 3a − 28

18. If 4 : x = 12 : 21, then x is:
(a) 5 (b) 6 (c) 7 (d) 8
Ans: (c) 7

19. If n(A) = 5 and n(B) = 3, then the maximum value of n(A ∪ B) is:
(a) 3 (b) 5 (c) 8 (d) 15
Ans: (c) 8

20. The Baudhāyana-Pythagoras Theorem is also known as:
(a) Sulba Sutra Theorem (b) Euclid’s Theorem (c) Thales Theorem (d) Ptolemy Theorem
Ans: (a) Sulba Sutra Theorem

✏️ SECTION B: Very Short Answers (5 × 2 = 10 Marks)

21. Evaluate: (6⁻² × 6⁴) ÷ 6³
Ans:
6⁻² × 6⁴ = 6²
6² ÷ 6³ = 6⁻¹ = 1/6

22. Write the expanded form of 3,047 using powers of 10.
Ans:
3047 = 3 × 10³ + 0 × 10² + 4 × 10¹ + 7 × 10⁰

23. Find the value of x in the Baudhāyana triple (x, 45, 51).
Ans:
x² + 45² = 51²
x² + 2025 = 2601
x² = 576
x = 24

24. If 9 books cost ₹405, find the cost of 13 books.
Ans:
Cost of 1 book = 405/9 = ₹45
Cost of 13 books = 45 × 13 = ₹585

25. If A = {p, q, r} and B = {q, r, s}, find A △ B (symmetric difference).
Ans:
A △ B = (A − B) ∪ (B − A)
= {p} ∪ {s} = {p, s}

📐 SECTION C: Short Answer Questions (6 × 3 = 18 Marks)

26. Simplify: (5x² − 3x + 7) + (2x² + 8x − 4) − (3x² − 2x + 1)
Ans:
= 5x² − 3x + 7 + 2x² + 8x − 4 − 3x² + 2x − 1
= (5x² + 2x² − 3x²) + (−3x + 8x + 2x) + (7 − 4 − 1)
= 4x² + 7x + 2

27. The angles of a quadrilateral are in the ratio 3 : 4 : 5 : 6. Find all the angles.
Ans:
Let angles = 3x, 4x, 5x, 6x
3x + 4x + 5x + 6x = 360°
18x = 360° → x = 20°
Angles = 60°, 80°, 100°, 120°

28. A garrison of 200 soldiers has food for 30 days. If 50 more soldiers join, how long will the food last?
Ans:
Total soldiers = 250
200 × 30 = 250 × x
6000 = 250x
x = 24 days

29. Verify whether (28, 45, 53) is a Baudhāyana triple.
Ans:
28² + 45² = 784 + 2025 = 2809
53² = 2809
LHS = RHS, so (28, 45, 53) is a Baudhāyana triple

30. Using distributive property, find 84 × 106.
Ans:
84 × 106 = (95 − 11)(95 + 11)
= 95² − 11²
= 9025 − 121 = 8904

31. In a bag, the ratio of red, blue, and green marbles is 4 : 5 : 6. If there are 180 marbles in total, find the number of each colour.
Ans:
Total parts = 4 + 5 + 6 = 15
Red = 180 × 4/15 = 48
Blue = 180 × 5/15 = 60
Green = 180 × 6/15 = 72

📏 SECTION D: Long Answer Questions (4 × 5 = 20 Marks)

32. Simplify: 3m(2m² − 4m + 5) − 2m²(m − 3) + 4m(m² − 2)
Ans:
= 6m³ − 12m² + 15m − 2m³ + 6m² + 4m³ − 8m
= (6m³ − 2m³ + 4m³) + (−12m² + 6m²) + (15m − 8m)
= 8m³ − 6m² + 7m

33. A 20 m ladder reaches a window 16 m above the ground. Find the distance of the foot of the ladder from the wall.
Ans:
Let base = x
x² + 16² = 20²
x² + 256 = 400
x² = 144
x = 12 m

34. A sum of ₹2,400 is divided among A, B, and C in the ratio 3 : 4 : 5. Find each share.
Ans:
Total parts = 3 + 4 + 5 = 12
Value of 1 part = 2400/12 = 200
A = 3 × 200 = ₹600
B = 4 × 200 = ₹800
C = 5 × 200 = ₹1000

35. Factorise: 8x² + 12x + 6xy + 9y
Ans:
= 4x(2x + 3) + 3y(2x + 3)
= (2x + 3)(4x + 3y)

📊 SECTION E: Case Study Questions (3 × 4 = 12 Marks)

Case Study 1

Read the passage and answer:

A fruit seller has apples, oranges, and bananas in the ratio 5 : 3 : 2. The total number of fruits is 500.

36. (a) Find the number of apples and oranges.
Ans:
Total parts = 5 + 3 + 2 = 10
Apples = 500 × 5/10 = 250
Oranges = 500 × 3/10 = 150

(b) Find the number of bananas.
Ans:
Bananas = 500 × 2/10 = 100

Case Study 2

Read the passage and answer:

In a right-angled triangle, the Baudhāyana-Pythagoras Theorem states that the square of the hypotenuse equals the sum of the squares of the other two sides.

37. (a) A right triangle has legs 11 cm and 60 cm. Find the hypotenuse.
Ans:
c² = 11² + 60²
= 121 + 3600 = 3721
c = √3721 = 61 cm

(b) If the hypotenuse is 65 cm and one leg is 25 cm, find the other leg.
Ans:
25² + b² = 65²
625 + b² = 4225
b² = 3600
b = 60 cm

Case Study 3

Read the passage and answer:

In a class of 60 students, 35 play Cricket, 30 play Football, and 15 play both Cricket and Football.

38. (a) How many students play only Cricket?
Ans:
Only Cricket = 35 − 15 = 20

(b) How many students play neither Cricket nor Football?
Ans:
n(C ∪ F) = 35 + 30 − 15 = 50
Neither = 60 − 50 = 10

🎯 Exam Tips for CBSE Class 8 Mathematics Students

🔢 Master exponent laws — they appear in every section

📐 Memorise angle properties of quadrilaterals and polygons

🧮 Use distributive property to simplify large calculations

📊 Read case studies twice before attempting

✅ Verify Baudhāyana triples by checking a² + b² = c²

🔗 Practise set operations like union, intersection, and difference

📞 Contact Dhingra Classes Today!

📍 Address: Plot No 3, XQ3G+H3M Deacon Homes, 301C, opp. Metro Zone, near Guru Govind Sing, Samarth Nagar, Dnyaneshwar Nagar, Pathardi Phata, Nashik, Maharashtra 422009

📱 Phone: 98230 62106

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